Criteria for regionally recurrent flows

Elaydi, Saber

doi:10.1090/S0002-9939-1982-0656124-6

Criteria for regionally recurrent flows
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Proc. Amer. Math. Soc. 85 (1982), 461-464 Request permission

Abstract:

Regionally recurrent and $P$-regionally recurrent flows are characterized in purely prolongational notions. An example is given to show that the condition $x \in J(x)$ is not, as many authors asserted, equivalent to regional recurrence.

References

Shair Ahmad and José Sarabia, On nonwandering continuous flows, Funkcial. Ekvac. 21 (1978), no. 3, 193–201. MR 540390
Saber Elaydi, $P$-recursion and transformation groups of characteristic $O$, J. Univ. Kuwait Sci. 9 (1982), no. 1, 1–9. MR 683034
Saber Elaydi, Weakly equicontinuous flows, Funkcial. Ekvac. 24 (1981), no. 3, 317–324. MR 655502
Saber Elaydi, On equicontinuous transformation groups, Bull. Austral. Math. Soc. 24 (1981), no. 3, 367–372. MR 647363, DOI 10.1017/S0004972700004901
S. Elaydi and S. K. Kaul, On characteristic $0$ and locally weakly almost periodic flows, Math. Japon. 27 (1982), no. 5, 613–624. MR 675560
Walter Helbig Gottschalk and Gustav Arnold Hedlund, Topological dynamics, American Mathematical Society Colloquium Publications, Vol. 36, American Mathematical Society, Providence, R.I., 1955. MR 0074810
Otomar Hájek, Prolongations in topological dynamics, Seminar on Differential Equations and Dynamical Systems, II (Univ. Maryland, College Park, Md., 1969) Lecture Notes in Math., Vol. 144, Springer, Berlin, 1970, pp. 79–89. MR 0394615
Ronald A. Knight, The center of a transformation group, Nonlinear phenomena in mathematical sciences (Arlington, Tex., 1980) Academic Press, New York, 1982, pp. 597–599. MR 728020
Ronald A. Knight, Prolongationally stable transformation groups, Math. Z. 161 (1978), no. 3, 189–194. MR 501165, DOI 10.1007/BF01214502